# turningpoint.test: The Turning Point Test of Statistical Independence In spgs: Statistical Patterns in Genomic Sequences

## Description

Perform a test of statistical independence of a data series by comparing the number of turning points present in the series with the number of turning points expected to be present in an i.i.d. series.

## Usage

 `1` ```turningpoint.test(x) ```

## Arguments

 `x` a numeric vector or univariate time series.

## Details

If the data is x[1], x[2], ..., x[n], then there is a turning point at the point i if either x[i-1]<x[i] and x[i]>x[i+1], or x[i-1]>x[i] and x[i]<x[i+1]. this function counts the number of turning points in the data, standardises it to have mean 0 and variance 1 and asymptotically tests it against a standard normal distribution. The test statistic is

T = (tp-mu)/sigma, where
tp is the number of turning points present in the series,
mu = 2*(n-2)/3,
sigma = sqrt((16*n-29)/90) and
n is the number of data points in the series.

The test is set up as follows:

H0: the data series is i.i.d. (not trending)
H1: the data series is not i.i.d. (trending)

## Value

A list with class "htest" containing the following components:

 `statistic` the value of the test statistic. `p.value` the p-value of the test. `method` a character string indicating what type of test was performed. `data.name` a character string giving the name of the data. `n` the number of points in the data series. `mu` The expected number of turning points that would be seen in an i.i.d. series. `sigma` The standard deviation of the number of turning points that would be seen in an i.i.d. series.

## Note

Missing values are not handled.

Points followed by a point having the exact same value are removed from the data series before computing the test statistic.

This test is useful for detecting cyclic/periodic trends in data series.

## Author(s)

Andrew Hart and Servet Mart<ed>nez

## References

Brockwell, Peter J., Davis, Richard A. (2002) Introduction to Time Series and Forecasting. Springer Texts in Statistics, Springer-Verlag, New York.

Bienaym<e9>, Ir<e9>n<e9>e-Jules (1874). Sur une question de probabilit<e9>s. Bull. Math. Soc. Fr. 2, 153-154.

`diffsign.test`, `rank.test`, `lb.test`, `markov.test`, `diid.test`

## Examples

 ```1 2 3``` ```#Generate an IID standard normal sequence n <- rnorm(1000) turningpoint.test(n) ```

### Example output

```	Turning point test of independence

data:  n
T = -0.40036, p-value = 0.6889
```

spgs documentation built on May 17, 2018, 1:04 a.m.